describing factorial effects
DESCRIPTION
Describing Factorial Effects. Kinds of means & kinds of effects Inspecting tables to describe factorial data patterns Inspecting line graphs to describe factorial data patterns Inspecting bar graphs to describe factorial data patterns Choosing among tables & graphs - PowerPoint PPT PresentationTRANSCRIPT
Describing Factorial Effects
• Kinds of means & kinds of effects
• Inspecting tables to describe factorial data patterns
• Inspecting line graphs to describe factorial data patterns
• Inspecting bar graphs to describe factorial data patterns
• Choosing among tables & graphs
• Other descriptions of factorial data patterns & interactions
Interpreting Factorial Results based on “Inspection”
Now that we have the basic language we will practice examining and describing main effects and interactions based on tables, line graphs and bar graphs portraying factorial results.
Once you know how to describe the results based on “inspection” it will be a very simple task to learn how to apply NHST to the process.
As in other designs we have looked at “an effect” as a numerical difference between two “things”, in factorial analyses…
Main effects involve differences between marginal means.
Simple effects involve differences between cell means.
Interactions involve the differences between simple effects.
Inspecting a Table to determine simple effects & interaction…
Task Presentation Paper Computer
Task Difficulty
Easy 90 90
Hard 50 70
We’ll look at describing the interaction using each set of simple effects in turn. Then we’ll look at describing each main effect (and checking if each is descriptive or misleading)
Inspecting a Table to determine simple effects & interaction…
Simple Effects of Task Presentation
Task PresentationTask Paper ComputerDifficulty
Easy 90 90
Hard 50 70
SE of Task Pres for EasyTasks
90 vs. 90 SE = 0
SE of Task Pres for HardTasks
50 vs. 70 SE = 20
There is an interaction of Task Difficulty and Task Presentation as they relate to performance. There is no effect of presentation for easy tasks, however for hard tasks computer presentations led to higher scores than did paper presentations.
Inspecting a Table to determine simple effects & interaction…
Simple Effects of Task Difficulty
Task Presentation Task Paper ComputerDifficulty
Easy 90 90
Hard 50 70
SE of Task Diff for Paper Pres.
90 vs. 50 SE = 40
SE of Task Diff for Computer Pres.
90 vs. 70 SE = 20
There is an interaction of Task Difficulty and Task Presentation as they relate to performance. Easy tasks are consistently performed better than hard tasks, however this effect is larger for paper presentations than for computer presentations.
Inspecting a Table to determine main effects …
marginal means for Task Difficulty Task Presentation 90 vs. 60 Easy > HardTask Paper ComputerDifficulty
Easy 90 90 90
Hard 50 70 60
This main effect is descriptive..
Easy > Hard for BOTH
Paper & Computer tasks
Overall, easy tasks were performed better than hard tasks.
Inspecting a Table to determine main effects …
marginal means for Task Presentation Task Presentation 70 vs. 80 Paper < ComputerTask Paper ComputerDifficulty
Easy 90 90
Hard 50 70
70 80
This main effect is potentially misleading ...
Paper < Computer only for hard tasks
Paper = Computer for easy tasks
Overall, there was better performance on computer than paper tasks. However, this was not descriptive for easy tasks.
Inspecting a line graph …
“Different differences” and “Differential Simple Effects” both translate into NONPARALLEL LINES in a figure.
Performance Key for Task Difficulty O = Easy X = Hard
90 O O
70 X
50 X
30
Paper Computer
Task Presentation P C
Easy 90 90
Hard 50 70
Inspecting a line graph to determine simple effects & interaction…
Performance
90 O O Simple Effects of Task Presentation
70 X
50 X
30
Paper Computer
Task Presentation
Key for Task Difficulty
O = Easy
X = Hard
SE of Task Pres for EasyTasks
90 vs. 90 SE = 0
SE of Task Pres for HardTasks
50 vs. 70 SE = 20
There is an interaction of Task Difficulty and Task Presentation as they relate to performance. There is no effect of presentation for easy tasks, however for hard tasks computer presentations led to higher scores than did paper presentations.
Inspecting a line graph to determine simple effects & interaction…
Performance
90 O O
70 X
50 X
30
Paper Computer
Task Presentation
Key for Task Difficulty
O = Easy X = Hard
Simple Effects of Task Difficulty
SE Task Diff for Paper Pres.
90 vs. 50 SE = 40
SE Task Diff for Computer Pres.
90 vs. 70 SE = 20
There is an interaction of Task Difficulty and Task Presentation as they relate to performance. Easy tasks are consistently performed better than hard tasks, however this effect is larger for paper presentations than for computer presentations.
How not to Inspect a line drawing to determine if there is an interaction…
This is a “cross-over” interaction -- it certainly IS an interaction
Performance but it IS NOT the only kind !!
90
70
50
30
Paper Computer
Task Presentation Key for Task Difficulty
Easy Hard
Inspecting a line graph to determine if there are main effects…
marginal means for Task Difficulty
Performance 90 vs. 60 Easy > Hard
90 O O
70 X
50 X
30
Paper Computer
Task Presentation
Key for Task Difficulty
O = Easy X = Hard
This main effect is descriptive..
Easy > Hard for BOTH
Paper & Computer tasks
Overall, easy tasks were performed better than hard tasks.
Inspecting a line graph to determine if there are main effects…
Performance marginal means for Task Pres 70 vs. 80 Paper < Computer
90 O O
70 X
50 X
30
Paper Computer
Task Presentation
Key for Task Difficulty
O = Easy X = Hard
This main effect is potentially misleading ...
Paper < Computer for hard tasks
but...
Paper = Computer for easy tasks
Overall, there was better performance on computer than paper tasks. However, this was not descriptive for easy tasks.
Inspecting a Bar Graph …
“Different differences” and “Differential Simple Effects” both translate into “different height differences” in a bar graph.
Performance
90
70
50
30
Easy Hard Easy Hard
Paper Computer P C
Task Presentation Easy 90 90
Hard 50 70
Inspecting a Bar Graph to determine simple effects & interaction… “Different differences” and “Differential Simple Effects” both translate into “different height differences” in a bar graph.
Performance Simple Effects of Task Difficulty
90
70
50 30 Easy Hard Easy Hard
Paper Computer
Task Presentation
SE Task Diff for Paper Pres.
90 vs. 50 SE = 40
SE Task Diff for Computer Pres.
90 vs. 70 SE = 20
There is an interaction of Task Difficulty and Task Presentation as they relate to performance. Easy tasks are consistently performed better than hard tasks, however this effect is larger for paper presentations than for computer presentations.
Inspecting a Bar Graph to determine simple effects & interaction…
“Different differences” and “Differential Simple Effects” both translate into “different height differences” in a bar graph.
Performance Simple Effects of Task Presentation
90
70
50 30 Easy Hard Easy Hard
Paper Computer
Task Presentation
SE of Task Pres for EasyTasks
90 vs. 90 SE = 0
SE of Task Pres for Hard Tasks
50 vs. 70 SE = 20
There is an interaction of Task Difficulty and Task Presentation as they relate to performance. There is no effect of presentation for easy tasks, however for hard tasks computer presentations led to higher scores than did paper presentations.
Inspecting a Bar graph to determine if there are main effects…
“Different differences” and “Differential Simple Effects” both translate into “different height differences” in a bar graph.
Performance marginal means for Task Presentation
70 vs. 80 Paper < Computer
90
70
50 30 Easy Hard Easy Hard
Paper Computer
Task Presentation
This main effect is potentially misleading ...
Paper < Computer for only for hard tasks
Paper = Computer for easy tasks
Overall, there was better performance on computer than paper tasks. However, this was not descriptive for easy tasks.
Inspecting a Bar graph to determine if there are main effects…
“Different differences” and “Differential Simple Effects” both translate into “different height differences” in a bar graph.
marginal means for Task Difficulty
Performance 90 vs. 60 Easy > Hard 90
70
50 30 Easy Hard Easy Hard
Paper Computer
Task Presentation
This main effect is descriptive..
Easy > Hard for BOTH
Paper & Computer tasks
Overall, easy tasks were performed better than hard tasks.
Choosing Among Tables, Line Graphs and Bar Graphs
Tables
• Provides more detail (exact means and standard deviations)
• Easier to see main effects (can include marginal means)
• Harder to see the interaction
Line Graphs
• Easier to see interaction pattern (than tables)
• Harder to see main effects (than tables)
• “Formally” limited to using when quantitative IV on X axis
Bar Graphs
• Interactions -- easier than tables, not as easy as line graphs
• Mains -- harder to see than tables
Note: Any of these can include std, or SEM “whiskers”
Sometimes our hypotheses aren’t about patterns of simple effects, but … are about other kinds of mean difference patterns…
The IVs are “Training Modality” and “Testing Modality” leading to this 2x2 factorial design…
VV
Training ModalityVisual Touch
VT TT
TV
Te
stin
g M
oda
lity
To
uch
V
isua
l
Among these conditions, 2 are “intramodal” (VV & TT) & 2 are “cross-modal” (VT & TV).
RH:s for the study were…RH1: VV > TT hypothesized dif among intramodal conditionsRH2: VT > TV hypothesized dif among cross-modal conditions
Neither of which corresponds to a “simple effect” !
VV
Training ModalityVisual Touch
VT
TT
TV
Te
stin
g M
oda
lity
Cro
ss
In
tra
In this case there is an “organizational” solution…Just re-label the IVs…“Training Modality” Vision vs. Touch & “Testing Modality” Intramodal vs. Cross-modal then…
RH1: VV > TT SE of Training Modality for Intramodal testsRH2: VT > TV SE of Training Modality for Cross-modal tests
Per
form
ance
99.6%
Training ModalityVisual Touch
26.2 %
Te
stin
g M
oda
lity
To
uch
V
isua
l25.6 %
24.8 %
… which can be directly & completely tested using the 6 pairwise comparisons among the 4 conditions.
VV VT TV TT
Another Example – same research area…
This was the common design for studying intra- and cross-modal memory with the usual RH: VV > VT > TV = TT
After several studies, someone noticed that these conditions define a factorial…
99.6%
Training ModalityVisual Touch
26.2 %
Te
stin
g M
oda
lity
To
uch
V
isua
l
25.6 %
24.8 %
There was an interaction!
There was a (misleading) main effect of Training Modality.
There was a (misleading) main effect of Testing Modality.
However interesting and informative was the idea from the significant interaction, that “performance is the joint effect of Training and Testing Modalities” – none of these “simple effect tests” give a direct test of the RH:
The set of 6 pairwise comparisons gives the most direct RH test!!!
Notice how the very large VV cell mean “drives” both main effects (while ensuring they will each be misleading) as well as driving the interaction!?!
“Describing a pattern of data that includes an interaction” vs.“Describing the Interaction in a pattern of data”
90 70 50 30
Paper Computer
Task Presentation
The pattern of data shown the figure demonstrate that while Task Presentation has no effect for Easy tasks, for Hard tasks, those using Computer did better than when using Paper.
This is “a description of a pattern of data that includes an interaction”
Technically, it would be wrong to say that “The interaction shown in the figure demonstrates that while Task Presentation has no effect for Easy tasks, for Hard tasks, those using Computer did better than when using Paper.
In order to “describe the interaction effect” we have to isolate the “interaction effect” from the main effects…
Easy
Hard
The process, called “mean polishing,” involves residulaizing the data for the main effects, leaving the interaction effect… Presentation Paper Comp means row effect
Easy 90 90 90 +15 Hard 50 70 60 -15 means 70 80 75 grand mean
col effect -5 +5
Correcting for row effects (subtract +/- 15)
Presentation Paper Comp
Easy 75 75 Hard 65 85
Correcting for column effects (subtract +/- 5)
Presentation Paper Comp
Easy 80 70 Hard 70 80
Correcting for Grand Mean (subtract 75)
Presentation Paper Comp
Easy 5 -5 Hard -5 5
10 5 0 -5 -10
Paper Computer
Task Presentation
Easy
Hard
The proper description of “the interaction effect” is
The interaction shown in the figure demonstrates that for Easy tasks those using Paper performed better than those using Computer, however, for Hard tasks, those using Computer performed better than those using Paper.
Hard
Easy
Hard
Looked at in this way, interactions differ in only 2 ways…
Which group has “increase” and which had “decrease”
Easy
Hard
vs.Easy
Hard
The “strength” of the interaction effect…
Easy
Hard
Easy
Hard
Easy
Hard
Easy
Hard
Easy
Hard
Easy
Hard
Easy
Hard
EasyEasy
Hard
Easy
Hard
null small medium large